How to keep the vertex normals after deleting an edge/face?
A single vertex can't have a normal vector. A normal is the vector which is perpendicular to two other vectors (edges) the normal is calculated using the cross product. 

A vertex normal is the average of all surfaces normals which contain a certain vertex, this does not mean that a vertex can have a normal. 

Perhaps you could move the original quads to another (invisible) layer.